Astronomy 23/223 Homework:

Orbits and Motions

 1. In this course, the primary unit of measure is an astronomical unit (AU). 1 AU = 149597870 km (or 1.4959787 X 1011 meters). Alpha Centauri, the nearest star system, is at a distance of 4.27 light years, where a light year is equal to 9.46073 X 1012 km. Calculate the distance to Alpha Centauri in AU. Assume the Earth is in a circular orbit at 1 AU from the Sun. Knowing that the orbital period is one year, compute the orbital speed of the Earth around the Sun. If a spacecraft traveled at this speed, how long would it take to reach Alpha Centauri? 2. Calculate the force of gravity between the Sun and the Moon. Now find the force between the Earth and the Moon. Which is greater? 3. From the data given below for the two asteroids 9273 Schloerb and 9274 Amylovell, Asteroid 9273 Schloerb has the following orbital elements: Semi-major axis = 2.4281216 AU Eccentricity = 0.155498 Inclination = 0.91601 degrees Asteroid 9274 Amylovell has the following orbital elements: Semi-major axis = 2.6338821 AU Eccentricity = 0.1568029 Inclination = 6.82047 degrees (a) Which has the longer orbital period? (b) Which is closest to the sun at perihelion? (c) Which is furthest from the the sun at aphelion? (d) Do either of these asteroids cross the orbit of the Mars (1.5 AU)? 4. Our Moon has an orbital period of 27.322 days, and a semi-major axis of 384,400 km. Use this information and what you know about the forces involved to estimate the mass of the Earth, and compare your result with a published value for the mass. 5. At what distance from Earth would a satellite be synchronized to our rotation period, such that it appeared to remain stationary in the sky? How does this compare to altitudes which can be reached by the Space Shuttle (which orbits every 90 minutes)?

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